Problem $2(8$ points$)$

In an initial survey designed to estimate the percentage of time air$-$express cargo loaders are idle, an

analyst found that loaders were idle in $8$ of the $50$ observations.

a$.$ What is the estimated percentage of idle time?

Estimated percentage of idle time:

Student name:

b$.$ Based on the initial results, approximately how many observations would you require to

estimate the actual percentage of idle time to within $7$ percent with a confidence of $99$

percent? $($Do not round intermediate calculations. Round up your final answer to the

next whole number.$)$